共查询到20条相似文献,搜索用时 15 毫秒
1.
Price's Law states that linear perturbations of a Schwarzschild black hole fall off as t−2?−3 for t→∞ provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially static (i.e., their time derivative is zero), then the decay is predicted to be t−2?−4. We give a proof of t−2?−2 decay for general data in the form of weighted L1 to L∞ bounds for solutions of the Regge–Wheeler equation. For initially static perturbations we obtain t−2?−3. The proof is based on an integral representation of the solution which follows from self-adjoint spectral theory. We apply two different perturbative arguments in order to construct the corresponding spectral measure and the decay bounds are obtained by appropriate oscillatory integral estimates. 相似文献
2.
We give a very general isoperimetric comparison theorem which, as an important special case, gives hypotheses under which the spherically symmetric -spheres of a spherically symmetric -manifold are isoperimetric hypersurfaces, meaning that they minimize -dimensional area among hypersurfaces enclosing the same -volume. This result greatly generalizes the result of Bray (Ph.D. thesis, 1997), which proved that the spherically symmetric 2-spheres of 3-dimensional Schwarzschild space (which is defined to be a totally geodesic, space-like slice of the usual -dimensional Schwarzschild metric) are isoperimetric. We also note that this Schwarzschild result has applications to the Penrose inequality in general relativity, as described by Bray.
3.
Huiya He 《Mathematische Nachrichten》2023,296(7):2838-2849
In this paper, we prove the three-dimensional conjecture with nonnegative Ricci curvature. Moreover, we establish rigidity theorems for three-dimensional compact, oriented, connected V-static metrics with nonnegative Ricci curvature. Finally, we obtain classification results on three-dimensional vacuum static space and Miao–Tam critical metric with nonnegative Ricci curvature. 相似文献
4.
Rohollah Bakhshandeh‐Chamazkoti 《Mathematical Methods in the Applied Sciences》2016,39(12):3163-3172
In this research article, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza–Klein black hole space‐time in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space‐time metric using Lie point symmetries is presented, and then the n‐dimensional optimal system of this space‐time metric, for n = 1,…,4, are computed. It is shown that there is no any n‐dimensional optimal system of Lie symmetry subalgebra associated to the system of geodesic for n≥5. Then the point symmetries of the one‐parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian that means Noether symmetries are found, and then the conservation laws associated to the system of geodesic equations are calculated via Noether's theorem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
Chengjie Yu 《Frontiers of Mathematics in China》2008,3(4):589-598
In this article, we provide a systematic method to construct examples of complete Ricci flat metrics on ℂP2, with three lines in the general position deleted by Hsieh [Proc. AMS, 1995, 123: 1873–1877] and generalize them to higher
dimensions. In addition, we further show that the examples of Hsieh are indeed all flat.
相似文献
6.
Eun Sun Choi 《Journal of Mathematical Analysis and Applications》2009,353(1):375-385
In the harmonic Bergman space with the normal weight, we prove norm equivalences in terms of radial, gradient and invariant gradient norms. Using this, we give new characterizations in terms of Lipschitz type conditions with Euclidean, pseudo-hyperbolic and hyperbolic metrics on the ball. 相似文献
7.
Abdelhadi Belkhirat Athanase Papadopoulos Marc Troyanov 《Transactions of the American Mathematical Society》2005,357(8):3311-3324
We define and study a natural weak metric on the Teichmüller space of the torus. A similar metric has been defined by W. Thurston on the Teichmüller space of higher genus surfaces and our definition is motivated by Thurston's definition. However, we shall see that in the case of the torus, this metric has a different behaviour than on higher genus surfaces.
8.
9.
10.
K. V. Navickis 《Lithuanian Mathematical Journal》2000,40(2):166-175
We consider intrinsic normalizations of distributions of flags of type (m, m+1) on the Grassmann manifold ofm-planes of a (2m+2)-dimensional projective space.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 214–227, April–June, 2000.
Translated by V. Mackevičius 相似文献
11.
K. V. Navickis 《Lithuanian Mathematical Journal》2000,40(3):258-268
We consider intrinsic normalizations of distributions of flags of type (m, m+1) on the Grassmann manifold ofm-planes of a (2m+2)-dimensional projective space.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 335–349, July–September, 2000.
Translated by V. Mackevičius 相似文献
12.
We construct a holomorphic Hermitian line bundle over the moduli space of stable triples of the form (E1, E2,?), where E1 and E2 are holomorphic vector bundles over a fixed compact Riemann surfaceX, and?: E2 → E1 is a holomorphic vector bundle homomorphism. The curvature of the Chern connection of this holomorphic Hermitian line bundle is computed. The curvature is shown to coincide with a constant scalar multiple of the natural Kähler form on the moduli space. The construction is based on a result of Quillen on the determinant line bundle over the space of Dolbeault operators on a fixed C∞ Hermitian vector bundle over a compact Riemann surface. 相似文献
13.
王香庆 《高校应用数学学报(A辑)》2004,19(4):471-478
在各类Besov空间中建立若干等价关系.文中的定理1是Cohen等人2000年论文中的定理4.2的实质性扩充,定理2将李松1997年论文中的定理7延拓到0
相似文献
14.
Tian Ma & Shouhong Wang 《数学研究》2014,47(4):305-378
First, the essence of a physical theory for a multilevel system is through
coupling different physical laws in different levels by a symmetry-breaking principle,
rather than through a unification using larger symmetry. In astrophysical dynamics,
the symmetry-breaking mechanism and the coupling are achieved by prescribing the
coordinate system so that the laws of fluid dynamics and heat conductivity are coupled
with gravitational field equations. Another important ingredient in modeling fluid
motion in astrophysics is to use the momentum density field to replace the velocity
field as the state function of cosmic objects. Second, by applying the new symmetry-breaking
mechanism and the new coupled astrophysical dynamics model, we rigorously
prove a basic theorem on black holes: Assume the validity of the Einstein theory
of general relativity, then black holes are closed, innate and incompressible. Third, we
prove a theorem on structure of universes. Assume the Einstein theory of general relativity,
and the principle of cosmological principle that the universe is homogeneous
and isotropic. Then we show that 1) all universes are bounded, are not originated from
a Big-Bang, and are static; and 2) The topological structure of our Universe can only
be the 3D sphere. Also, thanks to the basic properties of black holes, we show that our
results on our Universe resolve such fundamental problems as dark matter and dark
energy, redshifts and CMB. Fourth, we discovered that both supernovae explosion and AGN jets, as well as many astronomical
phenomena, are due to combined relativistic, magnetic and thermal effects.
The radial temperature gradient causes vertical Bénard convection cells, and the relativistic
viscous force (via electromagnetic, the weak and the strong interactions) gives
rise to an huge explosive radial force near the Schwarzschild radius, leading e.g. to
supernovae explosion and AGN jets. 相似文献
15.
本文研究B空间中无限时滞随机泛函微分方程解的估计.利用BDG不等式和It(o)公式及基本不等式,得到该方程解的p阶矩估计、样本Liapunov指数估计以及解的连续性等主要结果. 相似文献
16.
In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the composition operator to be compact on the Bloch space in a bounded symmetric domain. 相似文献
17.
We study infinitesimal properties of nonsmooth (nondifferentiable) functions on smooth manifolds. The eigenvalue function of a matrix on the manifold of symmetric matrices gives a natural example of such a nonsmooth function.
A subdifferential calculus for lower semicontinuous functions is developed here for studying constrained optimization problems, nonclassical problems of calculus of variations, and generalized solutions of first-order partial differential equations on manifolds. We also establish criteria for monotonicity and invariance of functions and sets with respect to solutions of differential inclusions.
18.
María J. Martín 《Journal of Mathematical Analysis and Applications》2005,304(1):22-32
We obtain new upper bounds on the norms of univalently induced composition operators acting on the Dirichlet space and compute explicitly the norms for univalent symbols whose range is the disk minus a set of measure zero. As an application, we show that the spectral radius of every univalently induced composition operator on the Dirichlet space is equal to one. 相似文献
19.
Extensions of the Nourdin-Peccati analysis to Rn-valued random variables are obtained by taking conditional expectation on the Wiener space. Several proof techniques are explored, from infinitesimal geometry, to quasi-sure analysis (including a connection to Stein's lemma), to classical analysis on Wiener space. Partial differential equations for the density of an Rn-valued centered random variable Z=(Z1,…,Zn) are obtained. Of particular importance is the function defined by the conditional expectation given Z of the auxiliary random matrix (−DL−1Zi|DZj), i,j=1,2,…,n, where D and L are respectively the derivative operator and the generator of the Ornstein-Uhlenbeck semigroup on Wiener space. 相似文献
20.
本文针对绝对关联度、综合关联度以及相对关联度的取值范围存在的不足,首先,设置了控制因子λ以及空间中的距离d,以此来调节关联度值的范围,建立了新模型。其次,研究了它的一些性质,并在理论上证明了新模型满足灰色关联公理。另外,提出了新模型的准优值所满足的几个原则,并结合灵敏性分析原理给出了准优值的算法步骤。最后,通过实例研究,验证了新模型所得结果不但能够使关联度的值扩充到(0,1]这一更大的范围,而且提高了区分度和分辨效果。 相似文献